Finite Group Databasebeta

← #22609140

Subgroups — #22609140

Order 9344.

208 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989294C211yesmaximal, characteristic
2#17988938C211yesmaximal, characteristic, complemented
3#17988873C211yesmaximal, characteristic, complemented
4#17988792C211yesmaximal, characteristic
5#17988335C211yesmaximal, characteristic, complemented
6#17988319C211yesmaximal, characteristic, complemented
7D4⋊C8×C73C211yesmaximal, characteristic
8C2×#11924016—21no—
9#14556591C2211yescharacteristic
10#14556591C2211yescharacteristic
11#14556582—21no—
12#14556570—21no—
13#14556568—22no—
14C4×Dic146C2211yescharacteristic
15D4×Dic73—21no—
16C2×C4⋊Dic73—21no—
17#14556523—21no—
18C4⋊#10596831C2211yescharacteristic
19#14556516—21no—
20#14556516—22no—
21#14556514—21no—
22C4×D4×C73C2211yescharacteristic
23C4⋊C8×C73C2211yescharacteristic
24C4×C8×C73C2211yescharacteristic
25C2×Dic146—21no—
26C2×Dic146D411yescharacteristic
27C2×Dic146D412yes—
28C22×Dic73—22no—
29#11924016—42no—
30C2×#10596831—21no—
31C4⋊Dic73—22no—
32C4⋊Dic73—21no—
33C4⋊Dic73—21no—
34C4⋊Dic73—21no—
35C4⋊Dic73—21no—
36C4⋊Dic73D411yescharacteristic
37#11924007—22no—
38#11924007—21no—
39C22⋊Dic73—22no—
40C4×Dic73—21no—
41C2×D4×C73D411yescharacteristic
42C22×C4×C73—21no—
43C2×C8×C73—21no—
44C2×C8×C73—21no—
45C4⋊C4×C73D411yescharacteristic
46C22⋊C4×C73—21no—
47C42×C73C2311yescharacteristic
48C23×C73—21no—
49D4×C73—21no—
50D4×C73SD1612yes—
51C2×C4×C73—21no—
52C2×C4×C73—41no—
53C2×C4×C73—41no—
54C2×C4×C73C2×D411yescharacteristic
55C2×C4×C73C2×D411yescharacteristic
56C2×C4×C73C2×D411yescharacteristic
57C2×Dic73—21no—
58C2×Dic73—21no—
59C2×Dic73—22no—
60C2×Dic73—41no—
61C2×Dic73—82no—
62Dic146—21no—
63Dic146—21no—
64Dic146—42no—
65Dic146—41no—
66Dic146—41no—
67C8×C73—41no—
68C8×C73—41no—
69#10596831—41no—
70C22×C73—22no—
71C22×C73—41no—
72C22×C73—41no—
73C22×C73#12011yescharacteristic
74C4×C73—21no—
75C4×C73—41no—
76C4×C73C2×SD1611yescharacteristic
77C4×C73#13511yescharacteristic
78C4×C73#13711yescharacteristic
79C4×C73#13711yescharacteristic
80Dic73—41no—
81Dic73—42no—
82Dic73—41no—
83Dic73—81no—
84C2×C73—42no—
85C2×C73#44811yescharacteristic
86C2×C73#45211yescharacteristic
87C2×C73#45511yescharacteristic
88#1643—731nomaximal, Sylow
89C73#164311yescharacteristic, complemented, Sylow
90#554—731no—
91#487—731no—
92#475—731no—
93#461—731no—
94#333—731no—
95Q8⋊C8—731no—
96D4⋊C8D7311yescharacteristic
97C2×SD16—1461no—
98C4⋊Q8—731no—
99C4⋊Q8—731no—
100#125—1461no—
101C22⋊Q8—1462no—
102C22⋊Q8—1461no—
103C4×Q8—731no—
104C4×D4—1461no—
105C4×D4C2×D7311yescharacteristic
106C2×C4⋊C4—1461no—
107#106—1461no—
108C4⋊C8—731no—
109C4⋊C8C2×D7311yescharacteristic
110#103—1461no—
111#103—1462no—
112#103—1461no—
113C4×C8C2×D7311yescharacteristic
114C2×Q8—732no—
115C2×Q8—731no—
116C2×Q8—1461no—
117C2×D4D29211yescharacteristic
118C22×C4—21no—
119C22×C4—1462no—
120SD16—2922no—
121C2×C8—21no—
122C2×C8—21no—
123C2×C8—1461no—
124C4⋊C4—731no—
125C4⋊C4—1462no—
126C4⋊C4—1462no—
127C4⋊C4—1461no—
128C4⋊C4—1461no—
129C4⋊C4—1461no—
130C4⋊C4—1461no—
131C4⋊C4—1461no—
132C4⋊C4D29211yescharacteristic
133C22⋊C4—21no—
134C22⋊C4—1462no—
135C42—1461no—
136C42C22×D7311yescharacteristic
137C23—21no—
138Q8—2922no—
139Q8—2921no—
140Q8—2921no—
141Q8—1461no—
142Q8—1461no—
143D4—21no—
144D4#1192401712yes—
145C2×C4—21no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—2921no—
149C2×C4—5842no—
150C2×C4—1461no—
151C2×C4—1461no—
152C2×C4—1462no—
153C2×C4D4×D7311yescharacteristic
154C2×C4D4×D7311yescharacteristic
155C2×C4C2×D29211yescharacteristic
156C8—41no—
157C8—41no—
158C8—2921no—
159C22—22no—
160C22—41no—
161C22—41no—
162C22#1455656111yescharacteristic
163C4—21no—
164C4—41no—
165C4—2921no—
166C4—2921no—
167C4—2922no—
168C4—5841no—
169C4C2×#1192401711yescharacteristic
170C4#1455661011yescharacteristic
171C4#1455662011yescharacteristic
172C4#1455662411yescharacteristic
173C2—42no—
174C2#1798872811yescharacteristic
175C2#1798875011yescharacteristic
176C2#1798876611yescharacteristic
subgroupG/H
centerC22#14556561
commutatorC42×C73C23
FrattiniC42C22×D73
FittingD4⋊C8×C73C2
socleC22×C73#120
hypercenterD4⋊C8D73
hypocenterC73#1643
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #17988938C2semidirect
3. #17988873C2semidirect
5. #17988335C2semidirect
6. #17988319C2semidirect
89. C73#1643semidirect